• KSII Transactions on Internet and Information Systems (TIIS)
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• 제15권12호
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• pp.4567-4583
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• 2021

This study proposes an analytical approximation algorithm based on extreme value theory (EVT) for the inverse of the power of the incomplete Gamma function. First, the Gumbel function is used to approximate the power of the incomplete Gamma function, and the corresponding inverse problem is transformed into the inversion of an exponential function. Then, using the tail equivalence theorem, the normalized coefficient of the general Weibull distribution function is employed to replace the normalized coefficient of the random variable following a Gamma distribution, and the approximate closed form solution is obtained. The effects of equation parameters on the algorithm performance are evaluated through simulation analysis under various conditions, and the performance of this algorithm is compared to those of the Newton iterative algorithm and other existing approximate analytical algorithms. The proposed algorithm exhibits good approximation performance under appropriate parameter settings. Finally, the performance of this method is evaluated by calculating the thresholds of space-time block coding and space-frequency block coding pattern recognition in multiple-input and multiple-output orthogonal frequency division multiplexing. The analytical approximation method can be applied to other related situations involving the maximum statistics of independent and identically distributed random variables following Gamma distributions.

• Advances in Computational Design
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• 제5권1호
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• pp.55-89
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• 2020

For the first time, an accurate analytical solution, based on coupled three-dimensional (3D) piezoelasticity equations, is presented for free vibration analysis of the angle-ply elastic and piezoelectric flat laminated panels under arbitrary boundary conditions. The present analytical solution is applicable to composite, sandwich and hybrid panels having arbitrary angle-ply lay-up, material properties, and boundary conditions. The modified Hamiltons principle approach has been applied to derive the weak form of governing equations where stresses, displacements, electric potential, and electric displacement field variables are considered as primary variables. Thereafter, multi-term multi-field extended Kantorovich approach (MMEKM) is employed to transform the governing equation into two sets of algebraic-ordinary differential equations (ODEs), one along in-plane (x) and other along the thickness (z) direction, respectively. These ODEs are solved in closed-form manner, which ensures the same order of accuracy for all the variables (stresses, displacements, and electric variables) by satisfying the boundary and continuity equations in exact manners. A robust algorithm is developed for extracting the natural frequencies and mode shapes. The numerical results are reported for various configurations such as elastic panels, sandwich panels and piezoelectric panels under different sets of boundary conditions. The effect of ply-angle and thickness to span ratio (s) on the dynamic behavior of the panels are also investigated. The presented 3D analytical solution will be helpful in the assessment of various 1D theories and numerical methods.

• Computers and Concrete
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• 제10권5호
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• pp.541-555
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• 2012

This paper presents an algorithm for the evaluation of stresses in reinforced concrete sections under service loads. The algorithm is applicable to any section defined by polygonal contours and is based on an analytical integration of the stresses. The nonlinear behaviour of concrete is represented by the parabola-rectangle law used in the Eurocode-2 for the ultimate concrete design. An integrated definition of the strains in concrete and steel is possible by the use of Heaviside functions, similarly to what is done for ultimate section design in Barros et al. (2004). Other constitutive equations for the definition of the stresses in the concrete or steel can be easily incorporated into the code. The examples presented consist in the evaluation of resulting axial load and bending moment in an irregular section and in a section in L shape. The results, for service stresses, can also be plotted in terms of design abacus; a rectangular doubly reinforced section is presented as example.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1993년도 한국자동제어학술회의논문집(국제학술편); Seoul National University, Seoul; 20-22 Oct. 1993
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• pp.524-529
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• 1993

Component Cost Analysis considers any given system driven by a white noise process as an interconnection of different components, and assigns a metric called "component cost" to each component. These component costs measure the contribution of each component to a predefined quadratic cost function. One possible use of component costs is for model reduction by deleting those components that have the smallest component cost. The theory of Component Cost Analysis is extended to include finite-bandwidth colored noises. The results also apply when actuators have dynamics of their own. When the dynamics of this input are added to the plant, which is to be reduced by CCA, the algorithm for model reduction process will be called Weighted Component Cost Analysis (WCCA). Closed-form analytical expressions of component costs for continuous time case, are also derived for a mechanical system described by its modal data. This is very useful to compute the modal costs of very high order systems beyond Lyapunov solvable dimension. A numerical example for NASA's MINIMAST system is presented.presented.

• Tribology and Lubricants
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• 제24권2호
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• pp.90-95
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• 2008

An elastic-plastic contact analysis is developed using a semi-analytical method. The elastic contact is solved within a Hertz theorem. The reciprocal theorem with initial strains is then introduced, to express the surface geometry as a function of contact stress and plastic strains. The irreversible nature of plasticity leads to an incremental formulation of the elastic-plastic contact problem, and an algorithm to solve this problem is set up. Closed form expression, which give residual stresses and surface displacements from plastic strains, are obtained by integration of the reciprocal theorem. The distribution of contact stress, residual stress and plastic strain are obtained by the changed surface geometry.

• Journal of the Optical Society of Korea
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• 제19권6호
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• pp.619-628
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• 2015

In this paper, we consider a method for estimating a stripe-type defect and the reconstruction of a defect-free L/S type mask used in lithography. Comparing diffraction patterns of defected and defect-free masks, we derive equations for the estimation of the location and size of the defect. We construct an analytical model for this problem and derive closed form equations to determine the location and size using phase retrieval problem solving techniques. Consequently, we develop an algorithm that determines a defect-free mask pattern. An example shows the validity of the equations.

• 대한전자공학회:학술대회논문집
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• 대한전자공학회 2000년도 ITC-CSCC -2
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• pp.673-676
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• 2000

Adaptive Fourier analysis of sinusoidal signals in noise is of essential importance in many engineering fields. So far, many adaptive algorithms have been developed for this purpose. In particular, a filter bank based algorithm called constrained notch Fourier transform of its cost-efficiency and easily controllable performance. However, its performance deteriorates when the signal frequencies are not uniformly spaced. This paper proposes, at first, a new structure for the CNFT, referred to as modified CNFT (MCNFT), to compensate the performance degeneration of the CNFT for noisy sinusoidal signals with non-uniformly spaced frequencies. Next, a detailed performance analysis for the MCNFT is conducted. Closed form expression of steady-state mean square error (MSE) for the discrete Fourier coefficients (DFCs) is derived. Extensive simulations are presented to demonstrate the improved performance of the MCNFT and the validity of the analytical results.

• 정보처리학회논문지B
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• 제16B권5호
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• pp.341-346
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• 2009

모션 데이터 글러브는 손의 움직임을 측정하여 컴퓨터에 입력하는 대표적인 인간과 컴퓨터간의 인터페이스 도구로서, 홈 오토에이션, 가상 현실, biometrics, 모션 캡쳐 등의 컴퓨터 신기술에 사용되는 필수 장비이다. 본 논문에서는 대중화를 위하여, 별도의 특수 장비 없이 사용 가능한 저가형 비주얼 모션 데이터 글러브를 개발하고자 한다. 본 방식의 특징은 기존의 모션 데이터 글러브에 사용되었던, 고가의 모션 센싱 섬유를 사용하지 않음으로써, 저가형으로 개발이 가능하다는 것이다. 따라서 제작이 용이하고 대중화에 크게 기여할 수 있다는 장점을 가진다. 본 방식에서는 모션 센싱 섬유를 사용하는 기계적인 방식대신 광학적 모션 캡쳐 기술을 개량한 비주얼 방식을 채택한다. 기존의 비주얼 방식에 비해 본 방식은 다음과 같은 장점과 독창성을 가진다. 첫째, 기존의 비주얼 방식은 가려짐 현상을 제거하고 3차원 자세 복원을 위해 많은 수의 카메라와 장비를 사용하는 데 비해, 본 방식은 모노비전 방식을 채택하여 장비가 간소하고 저가형 개발이 가능하다. 둘째, 기존의 모노비전방삭은 가려짐 현상에 취약하여 영상에서 가려진 부분은 3차원 자세 복원이 어려웠다. 하지만 본 논문은 독창적으로 설계된 막대 모양의 지시자를 사용하여, 영상에서 가려진 부분도 3차원 자세 복원이 가능하다. 셋째, 기존의 모노 비전 방식은 비선형 수치해석 형태의 영상 해석 알고리즘을 사용하는 경우가 많아서 초기화나 계산시간 면에서 불편하였다. 하지만, 본 논문에서는 독창적인 공식화 방법을 사용하여 닫힌 형태의 영상해석 알고리즘을 도출함으로써 이와 같은 불편을 개선하였다. 넷째, 기존의 닫힌 형태의 알고리즘은 공식화 과정에서 근사화 방법을 도입하는 경우가 많아서 정확도가 떨어지고 특이점에 의한 응용분야에 제한이 있었다. 하지만 본 방식은 오일러 각과 같은 국부적인 매개화나 근사화 등을 사용하는 대신 지수형태의 트위스트좌표계를 사용하는 독창적인 공식화 방법을 사용하여, 공식화 단계에서의 근사화 방법 없이 닫힌 형태의 알고리즘을 도출함으로써 이 문제들을 개선하였다.

• Smart Structures and Systems
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• 제17권2호
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• pp.231-256
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• 2016

This study concerns the derivation of optimum tuning formulas for a passive Tuned Mass Damper (TMD) device, for the case of benchmark ideal excitations acting on a single-degree-of-freedom (SDOF) damped primary structure. The free TMD parameters are tuned first through a non-linear gradient-based optimisation algorithm, for the case of harmonic or white noise excitations, acting either as force on the SDOF primary structure or as base acceleration. The achieved optimum TMD parameters are successively interpolated according to appropriate analytical fitting proposals, by non-linear least squares, in order to produce simple and effective TMD tuning formulas. In particular, two fitting models are presented. The main proposal is composed of a simple polynomial relationship, refined within the fitting process, and constitutes the optimum choice. A second model refers to proper modifications of literature formulas for the case of an undamped primary structure. The results in terms of final (interpolated) optimum TMD parameters and of device effectiveness in reducing the structural dynamic response are finally displayed and discussed in detail, showing the wide and ready-to-use validity of the proposed optimisation procedure and achieved tuning formulas. Several post-tuning trials have been carried out as well on SDOF and MDOF shear-type frame buildings, by confirming the effective benefit provided by the proposed optimum TMD.

• Computers and Concrete
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• 제27권4호
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• pp.319-332
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• 2021

The performance of gene expression programming (GEP) in predicting the compressive strength of bacteria-incorporated geopolymer concrete (GPC) was examined in this study. Ground-granulated blast-furnace slag (GGBS), new bacterial strains, fly ash (FA), silica fume (SF), metakaolin (MK), and manufactured sand were used as ingredients in the concrete mixture. For the geopolymer preparation, an 8 M sodium hydroxide (NaOH) solution was used, and the ambient curing temperature (28℃) was maintained for all mixtures. The ratio of sodium silicate (Na2SiO3) to NaOH was 2.33, and the ratio of alkaline liquid to binder was 0.35. Based on experimental data collected from the literature, an evolutionary-based algorithm (GEP) was proposed to develop new predictive models for estimating the compressive strength of GPC containing bacteria. Data were classified into training and testing sets to obtain a closed-form solution using GEP. Independent variables for the model were the constituent materials of GPC, such as FA, MK, SF, and Bacillus bacteria. A total of six GEP formulations were developed for predicting the compressive strength of bacteria-incorporated GPC obtained at 1, 3, 7, 28, 56, and 90 days of curing. 80% and 20% of the data were used for training and testing the models, respectively. R2 values in the range of 0.9747 and 0.9950 (including train and test dataset) were obtained for the concrete samples, which showed that GEP can be used to predict the compressive strength of GPC containing bacteria with minimal error. Moreover, the GEP models were in good agreement with the experimental datasets and were robust and reliable. The models developed could serve as a tool for concrete constructors using geopolymers within the framework of this research.